利用空间相关支撑集的协作稀疏回归——在高光谱解混中的应用
Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing
AI总结：
该研究提出一种结合空间相关支撑集先验的贝叶斯协作稀疏回归方法，用于高光谱图像线性解混，通过自适应MCMC算法估计物质存在概率与丰度，无需手动调参，经合成与真实数据验证性能优异。
摘要：
本文提出了一种新的贝叶斯协作稀疏回归方法，用于高光谱图像的线性解混。我们的贡献分为两部分：首先，我们提出了一种新的结构化稀疏回归贝叶斯模型，其中稀疏丰度向量的支撑集在像素间具有先验空间相关性（即物质在空间上是有序组织的，而非在像素层面随机分布）。该先验信息通过截断多元Ising马尔可夫随机场编码到模型中，同时考虑了像素不能为空（即每个像素中至少存在一种物质），以及不同物质可能呈现不同程度空间规律性的事实。其次，我们提出了一种先进的马尔可夫链蒙特卡罗算法，用于估计每种物质在每个像素中存在或不存在的后验概率，并在支撑集的最大边际后验配置条件下，计算丰度向量的最小均方误差（MMSE）估计。该算法的一个显著特性是能够自动调整马尔可夫随机场的参数值，从而使从业者无需通过交叉验证设置正则化参数。最后，我们通过一系列合成数据和真实数据实验，并与文献中的其他算法进行比较，验证了所提方法的性能。
英文摘要：
This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the supports of the sparse abundance vectors are a priori spatially correlated across pixels (i.e., materials are spatially organised rather than randomly distributed at a pixel level). This prior information is encoded in the model through a truncated multivariate Ising Markov random field, which also takes into consideration the facts that pixels cannot be empty (i.e, there is at least one material present in each pixel), and that different materials may exhibit different degrees of spatial regularity. Secondly, we propose an advanced Markov chain Monte Carlo algorithm to estimate the posterior probabilities that materials are present or absent in each pixel, and, conditionally to the maximum marginal a posteriori configuration of the support, compute the MMSE estimates of the abundance vectors. A remarkable property of this algorithm is that it self-adjusts the values of the parameters of the Markov random field, thus relieving practitioners from setting regularisation parameters by cross-validation. The performance of the proposed methodology is finally demonstrated through a series of experiments with synthetic and real data and comparisons with other algorithms from the literature.
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